NAME

newton -- Newton nonlinear algorithm

DESCRIPTION

Nonlinear Newton algorithm for the resolution of the following problem:
F(u) = 0
A simple call to the algorithm writes:
my_problem P;
field uh (Vh);
newton (P, uh, tol, max_iter);
The my_problem class may contains methods for the evaluation of F (aka residue) and its
derivative:
class my_problem {
public:
my_problem();
field residue (const field& uh) const;
Float dual_space_norm (const field& mrh) const;
void update_derivative (const field& uh) const;
field derivative_solve (const field& mrh) const;
};
The dual_space_norm returns a scalar from the weighted residual field term mrh returned by
the residue function: this scalar is used as stopping criteria for the algorithm. The
update_derivative and derivative_solver members are called at each step of the Newton
algorithm. See the example p_laplacian.h in the user's documentation for more.